Name: Pankaj Mani Dahal
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Tuesday, May 12, 2009
Special theory of relativity
Special relativity (SR) (also known as the special theory of relativity or STR) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz and Henri Poincare and others) in the paper "On the Electrodynamics of moving bodies". It generalizes Galileo's principle of relativity–that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames)–from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be. Special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source.
This theory has a wide range of consequences which have been experimentally verified, including counter-intuitive ones such as length contraction, time dilation and relativity of simultaneity, contradicting the classical notion that the duration of the time interval between two events is equal for all observers. (On the other hand, it introduces the space-time interval, which is invariant.) Combined with other laws of physics, the two postulates of special relativity predict the equivalence of matter and energy, as expressed in the mass-energy equivalence formula E = mc2, where c is the speed of light in a vacuum. The predictions of special relativity agree well with Newtonian mechanics in their common realm of applicability, specifically in experiments in which all velocities are small compared to the speed of light.
The theory is termed "special" because it applies the principle of relativity only to frames in uniform relative motion. Einstein developed general relativity to apply the principle more generally, that is, to any frame so as to handle general coordinate transformations, and that theory includes the effects of gravity. From the theory of general relativity it follows that special relativity will still apply locally (i.e. to the first order) to observers moving on arbitrary trajectories, and hence to any relativistic situation where gravity is not a significant factor.
Special relativity reveals that c is not just the velocity of a certain phenomenon, namely the propagation of electromagnetic radiation (light)—but rather a fundamental feature of the way space and time are unified as spacetime. A consequence of this is that it is impossible for any particle that has mass to be accelerated to the speed of light.
This theory has a wide range of consequences which have been experimentally verified, including counter-intuitive ones such as length contraction, time dilation and relativity of simultaneity, contradicting the classical notion that the duration of the time interval between two events is equal for all observers. (On the other hand, it introduces the space-time interval, which is invariant.) Combined with other laws of physics, the two postulates of special relativity predict the equivalence of matter and energy, as expressed in the mass-energy equivalence formula E = mc2, where c is the speed of light in a vacuum. The predictions of special relativity agree well with Newtonian mechanics in their common realm of applicability, specifically in experiments in which all velocities are small compared to the speed of light.
The theory is termed "special" because it applies the principle of relativity only to frames in uniform relative motion. Einstein developed general relativity to apply the principle more generally, that is, to any frame so as to handle general coordinate transformations, and that theory includes the effects of gravity. From the theory of general relativity it follows that special relativity will still apply locally (i.e. to the first order) to observers moving on arbitrary trajectories, and hence to any relativistic situation where gravity is not a significant factor.
Special relativity reveals that c is not just the velocity of a certain phenomenon, namely the propagation of electromagnetic radiation (light)—but rather a fundamental feature of the way space and time are unified as spacetime. A consequence of this is that it is impossible for any particle that has mass to be accelerated to the speed of light.
Einsteins general relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravity in modern physics. It unifies special relativity and Newton's law of universal gravitation, and describes gravity as a property of the geometry of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.
The predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Examples of such differences include gravitational time dilation, the gravitational redshift of light, and the gravitational time delay. General relativity's predictions have been confirmed in all observations and experiments to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory that is consistent with experimental data. However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity.
Einstein's theory has important astrophysical implications. It points towards the existence of black holes—regions of space in which space and time are distorted in such a way that nothing, not even light, can escape—as an end-state for massive stars. There is evidence that such stellar black holes as well as more massive varieties of black hole are responsible for the intense radiation emitted by certain types of astronomical objects such as active galactic nuclei or microquasars. The beending of light by gravity can lead to the phenomenon of gravitational lensing, where multiple images of the same distant astronomical object are visible in the sky. General relativity also predicts the existence of gravitational waves, which have since been measured indirectly; a direct measurement is the aim of projects such as LIGO. In addition, general relativity is the basis of current cosmological models of a consistently expanding universe.
The predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Examples of such differences include gravitational time dilation, the gravitational redshift of light, and the gravitational time delay. General relativity's predictions have been confirmed in all observations and experiments to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory that is consistent with experimental data. However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity.
Einstein's theory has important astrophysical implications. It points towards the existence of black holes—regions of space in which space and time are distorted in such a way that nothing, not even light, can escape—as an end-state for massive stars. There is evidence that such stellar black holes as well as more massive varieties of black hole are responsible for the intense radiation emitted by certain types of astronomical objects such as active galactic nuclei or microquasars. The beending of light by gravity can lead to the phenomenon of gravitational lensing, where multiple images of the same distant astronomical object are visible in the sky. General relativity also predicts the existence of gravitational waves, which have since been measured indirectly; a direct measurement is the aim of projects such as LIGO. In addition, general relativity is the basis of current cosmological models of a consistently expanding universe.
Black HOLE
In general relativity, a black hole is a region of space in which the gravitational field is so powerful that nothing, including light, can escape its pull. The black hole has a one-way surface, called an event horizon, into which objects can fall, but out of which nothing can come. It is called "black" because it absorbs all the light that hits it, reflecting nothing, just like a perfect blackbody in thermodynamics. Quantum analysis of black holes shows them to possess a temperature and radiate like black bodies.
Despite its invisible interior, a black hole can reveal its presence through interaction with other matter. A black hole can be inferred by tracking the movement of a group of stars that orbit a region in space which looks empty. Alternatively, one can see gas falling into a relatively small black hole, from a companion star. This gas spirals inward, heating up to very high temperature and emitting large amounts of radiation that can be detected from earthbound and earth-orbiting telescopes. Such observations have resulted in the general scientific consensus that, barring a breakdown in our understanding of nature, black holes do exist in our universe.
Despite its invisible interior, a black hole can reveal its presence through interaction with other matter. A black hole can be inferred by tracking the movement of a group of stars that orbit a region in space which looks empty. Alternatively, one can see gas falling into a relatively small black hole, from a companion star. This gas spirals inward, heating up to very high temperature and emitting large amounts of radiation that can be detected from earthbound and earth-orbiting telescopes. Such observations have resulted in the general scientific consensus that, barring a breakdown in our understanding of nature, black holes do exist in our universe.
Physics
Gravitational field contradiction
By Newton's theory, a gravitational field is no way dependent on the motion of matter. Thus the gravitational fields of a revolving sphere and a sphere at rest are perfectly identical provided their masses are equal. By Einstein's theory, this is not so: the gravitational fields of the two spheres differ slightly. What is the difference?
The most illustrative (if somewhat oversimplified) picture of this difference is the rotating body surrounded by an additional vortex gravitational field which entrains all bodies into circular motion. Another illustration would be to say that layers of space slowly revolve around the body, with the angular velocity of rotation being a function of distance: it is low far from the body and increases as we move closer to it.
By Newton's theory, a gravitational field is no way dependent on the motion of matter. Thus the gravitational fields of a revolving sphere and a sphere at rest are perfectly identical provided their masses are equal. By Einstein's theory, this is not so: the gravitational fields of the two spheres differ slightly. What is the difference?
The most illustrative (if somewhat oversimplified) picture of this difference is the rotating body surrounded by an additional vortex gravitational field which entrains all bodies into circular motion. Another illustration would be to say that layers of space slowly revolve around the body, with the angular velocity of rotation being a function of distance: it is low far from the body and increases as we move closer to it.
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